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(x+1)(x+9)=(x+3)(x+5)

less than a minute read Jun 16, 2024
(x+1)(x+9)=(x+3)(x+5)

Solving the Equation: (x+1)(x+9) = (x+3)(x+5)

This equation involves expanding both sides and then solving for x. Let's break down the steps:

1. Expand both sides of the equation:

  • (x+1)(x+9): Using the FOIL method (First, Outer, Inner, Last) we get:
    • x² + 9x + x + 9 = x² + 10x + 9
  • (x+3)(x+5): Similarly, we get:
    • x² + 5x + 3x + 15 = x² + 8x + 15

Now, our equation becomes: x² + 10x + 9 = x² + 8x + 15

2. Simplify the equation:

  • Subtract x² from both sides:
    • 10x + 9 = 8x + 15
  • Subtract 8x from both sides:
    • 2x + 9 = 15
  • Subtract 9 from both sides:
    • 2x = 6

3. Solve for x:

  • Divide both sides by 2:
    • x = 3

Solution:

Therefore, the solution to the equation (x+1)(x+9) = (x+3)(x+5) is x = 3.

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